Government plans for saving £350m a year in legal aid expenses suffered fresh defeats in the House of Lords after peers overturned a series of cost-saving proposals.

Peers voted by 237 to 198 to preserve legal aid for appeals against welfare benefit decisions, defeating reforms proposed in the legal aid, sentencing and punishment of offenders bill.

The amendment had been tabled by the Liberal Democrat Lady Doocey with support from Labour, Conservative and crossbench peers.

A second amendment, tabled by the Lord Newton, the former social security minister under Margaret Thatcher, ensured that legal aid should be available for higher-tier benefit appeals was also passed.

The votes came at the end of a two-hour debate during which every single speaker in the upper chamber – apart from the minister – opposed the Ministry of Justice plans. Peers from all parties questioned whether the proposed savings would be made.

Earlier Lord McNally, the Liberal Democrat justice minister, warned that if the government lost on the issue of providing legal aid on welfare benefit issues and support for advice centres it would "tear out the heart of the rationale of the bill".

The defeats will add to the pressure on the government's parliamentary timetable. The coalition is expected to try and reverse the Lords' decisions in the House of Commons on the grounds that the bill is primarily a financial measure.

Proposing her amendment, Doocey said: "If claimants are denied legal aid, their situation will get worse. This amendment would allow some of the most vulnerable people in society to fight for the benefits for which they are entitled."

Not-for-profit advice centres that help the most vulnerable in society would lose £51m a year under the cuts introduced by the bill, she warned.

Lord Newton cautioned that: "This process of change in legal aid is not taking place in a vacuum. It's during turbulence in the benefit system." More than 1 million people were likely to be adversely affected by changes to benefit under the welfare reform bill, he said.

"If I was still an MP I would be a bit worried. That's 2,000 people per constituency and they will all have relatives … and many others will be upset.

"There are a lot of people in this country to whom £10 or £20 a week makes a big difference as to whether they can heat [their homes] or eat. No one actually believes that the savings claimed by the government will be realised."

Advice centres will lose funding despite government promises of support, Lord Newton added. "I would not want to back off this amendment on the vague promise that something might be done in future."

The Liberal Democrat Lord Carlile asked: "At the end of the day are we going to make any savings in legal aid if people have to present their own cases or they end up in the hands of the mental health services? It's very likely there will be a negative impact in public funding."

Lord Goldsmith, the former Labour attorney general, said the damage inflicted on advice centres would be far-reaching. "The funding for the not-for-profit centres will be cut by 77%. The advice services alliance estimates that 800 specialist advice centres will lost as a result. The welfare benefits side requires an expertise which most lawyers don't have."

The government may be targeting so-called "fat cat lawyers", Lord Goldsmith noted, "but no cat gets fat on welfare law".

Lord Bach, the Labour justice spokesman in the Lords, said: "There is [now] access to justice for everyone, including the poor and the marginalised. We have a system that is both practical and principled. It's not perfect but it works. This bill will decimate it: 650,000 people who have access to justice will not have it any longer.

"It verges on being unconstitutional because it reduces access to justice. It will not save costs further down the line. If we do this we will be making our country a less civilised place."

McNally insisted: "The government is committed to ensuring that not-for-profit advice remains to provide claimants with means of how they can seek redress. It's not the case that legal aid is required in all cases."

A forthcoming review by the Cabinet Office will "secure the long-term sustainability of the not-for-profit advice sector" through additional funding, he added.

The opposition had painted "doomsday scenarios", MacNally said. "We have to take tough decisions in tough times. You lose control your economy you go into another round of cuts." The Labour opposition would also have had to make similar cuts, he noted.

Commenting on the vote to retain legal aid for welfare benefit appeals, the shadow justice secretary, Sadiq Khan, said: "This victory provides a vital safety net for the poorest in our society. It ensures that when bureaucrats make a mistake that denies support such as disability benefits to the vulnerable and their families, then they will have expert advice in making an appeal.

"According to Citizens Advice, every £1 of taxpayer money spent on legal aid in benefit cases saves the state up to £8.80 down the line.

"So, regardless of the Government's spin, today's vote is also about saving the taxpayer money through early stage intervention, of the kind that prevents problems escalating, reducing the call on resources in future months and years."

Richard Hawkes, chief executive of the disability charity Scope, said: "Thousands of disabled people and their families will be delighted at the action taken by Peers in the House of Lords today.

"The Lords have recognised that to cut legal aid at a time of unprecedented changes to welfare support would have meant disabled people who fall foul of poor decision-making, red tape or administrative error would have been pushed even further into poverty as they struggled to manoeuvre the complicated legal system without the necessary expert support they need.

"The result would have been a ticking time bomb of poorly prepared and lengthy tribunals and appeals, choking the courts and not saving money as suggested by Ken Clarke, but actually costing the Government far more in the long term."